Slide 1Holt McDougal Geometry
7-3 Triangle Similarity: AA, SSS, SAS 7-3 Triangle Similarity: AA, SSS, SAS
Holt Geometry
Warm Up
Lesson Presentation
Lesson Quiz
Warm Up Solve each proportion.
1. 2. 3.
angles and write 3 proportions using pairs of
corresponding sides.
Holt McDougal Geometry
7-3 Triangle Similarity: AA, SSS, SAS
Prove certain triangles are similar by using AA, SSS, and SAS.
Use triangle similarity to solve problems.
Objectives
7-3 Triangle Similarity: AA, SSS, SAS
There are several ways to prove certain triangles are similar. The following postulate, as well as the SSS and SAS Similarity Theorems, will be used in proofs just as SSS, SAS, ASA, HL, and AAS were used to prove triangles congruent.
Holt McDougal Geometry
Example 1: Using the AA Similarity Postulate
Explain why the triangles are similar and write a similarity statement.
Since , B E by the Alternate Interior Angles Theorem. Also, A D by the Right Angle Congruence Theorem. Therefore ABC ~ DEC by AA~.
Holt McDougal Geometry
Check It Out! Example 1
Explain why the triangles are similar and write a similarity statement.
By the Triangle Sum Theorem, m C = 47°, so C F.
B E by the Right Angle Congruence Theorem. Therefore, ABC ~ DEF by AA ~.
Holt McDougal Geometry
Holt McDougal Geometry
Holt McDougal Geometry
Example 2A: Verifying Triangle Similarity
Verify that the triangles are similar.
PQR and STU
Holt McDougal Geometry
Example 2B: Verifying Triangle Similarity
DEF and HJK
D H by the Definition of Congruent Angles.
Therefore DEF ~ HJK by SAS ~.
Holt McDougal Geometry
Check It Out! Example 2
Verify that TXU ~ VXW.
Therefore TXU ~ VXW by SAS ~.
Holt McDougal Geometry
7-3 Triangle Similarity: AA, SSS, SAS
A A by Reflexive Property of , and B C since they are both right angles.
Example 3: Finding Lengths in Similar Triangles
Explain why ABE ~ ACD, and then find CD.
Step 1 Prove triangles are similar.
Therefore ABE ~ ACD by AA ~.
Holt McDougal Geometry
Example 3 Continued
Corr. sides are proportional. Seg. Add. Postulate.
Substitute x for CD, 5 for BE, 3 for CB, and 9 for BA.
Cross Products Prop. x(9) = 5(3 + 9)
Simplify. 9x = 60
Holt McDougal Geometry
Check It Out! Example 3
Explain why RSV ~ RTU and then find RT.
Step 1 Prove triangles are similar.
It is given that S T. R R by Reflexive Property of .
Therefore RSV ~ RTU by AA ~.
Holt McDougal Geometry
Step 2 Find RT.
Corr. sides are proportional.
Substitute RS for 10, 12 for TU, 8 for SV.
Cross Products Prop.
RT(8) = 10(12)
8RT = 120
RT = 15